Till KTH:s startsida Till KTH:s startsida

Recitations

Recitation material

Problems for all recitations (pdf)

Solutions for all recitations (pdf)

Recitation 1 material

Detailed Solutions to the exercises (to be updated BEFORE each recitation)

Detailed solutions Recitations 8

Detailed solutions Recitation 9

Detailed solutions Recitation 10

Detailed solution Recitation 11

Recitation plan

Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.

R1 Probability theory - overview

R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)

R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)

R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)

R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7

R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)

R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)

R8 Method of stages (Ch. 9 : 9.1, 9.2, Exam 4.a. Suggestion for home exercise: Exam 6.)

R9 M/G/1 (Ch. 10: 10.1a,b, 10.2a, 10.4, Exam 9.a. Suggestion for home exercise: 10.3, 10.5a, Exam 5  )

R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, ... and a problem that is missing from the compendium problem on vacation systems (11.5))

R11 Queuing networks (Ch. 12:  12.2, 12.3 )

R12 Course summary, example exam problems

Exam problems solved on the recitations 

During the second part of the course we will solve an exam problem on most of the recitations,  to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.

 


  

Viktoria Fodor skapade sidan 3 september 2013

Ioannis Glaropoulos redigerade 28 januari 2014

Recitation material

Problems for all recitations (pdf)

Solutions for all recitations (pdf)

Detailed Solutions to the exercises (to be updated atbefore each recitation)

Recitation plan

Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.

R1 Probability theory - overview

R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)

R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)

R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)

R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7

R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)

R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)

R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)

R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)

R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )

R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )

R12 Course summary, example exam problems

Exam problems solved on the recitations 

During the second part of the course we will solve an exam problem on most of the recitations,  to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.

 

  

Ioannis Glaropoulos redigerade 12 februari 2014

Recitation material

Problems for all recitations (pdf)

Solutions for all recitations (pdf)

Detailed Solutions to the exercises (to be updated BEFORE each recitation)

Recitation plan

Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.

R1 Probability theory - overview

R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)

R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)

R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)

R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7

R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)

R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)

R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)

R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)

R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )

R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )

R12 Course summary, example exam problems

Exam problems solved on the recitations 

During the second part of the course we will solve an exam problem on most of the recitations,  to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.

 

  

Ioannis Glaropoulos redigerade 13 februari 2014

Recitation material

Problems for all recitations (pdf)

Solutions for all recitations (pdf)

Detailed Solutions to the exercises (to be updated BEFORE each recitation)

Recitation plan

Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.

R1 Probability theory - overview

R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)

R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)

R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)

R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7

R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)

R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)

R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)

R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)

R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )

R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )

R12 Course summary, example exam problems

Exam problems solved on the recitations 

During the second part of the course we will solve an exam problem on most of the recitations,  to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.